We consider the existence in arbitrary finite dimensions d of a POVM comprised d^2 rank-one operators all whose operator inner products are equal. Such set is called ``symmetric, informationally complete'' (SIC-POVM) and equivalent to equiangular lines C^d. SIC-POVMs relevant for quantum state tomography, cryptography, foundational issues mechanics. construct two, three, four. further conjecture that particular kind group-covariant SIC-POVM exists dimensions, providing numerical results up...

The ideas of thermodynamics have proved fruitful in the setting quantum information theory, particular notion that when allowed transformations a system are restricted, certain states become useful resources with which one can prepare previously inaccessible states. theory entanglement is perhaps best-known and most well-understood resource this sense. Here we return to basic questions using formalism theories developed show free energy emerges naturally from energy-preserving...

We conjecture a new entropic uncertainty principle governing the entropy of complementary observations made on system given side information in form quantum states, generalizing relation Maassen and Uffink [Phys. Rev. Lett. 60, 1103 (1988)]. prove special case for certain conjugate observables by adapting similar result found Christandl Winter pertaining to channels [IEEE Trans. Inf. Theory 51, 3159 (2005)], discuss possible applications this decoupling systems security analysis cryptography.

We describe some applications of quantum information theory to the analysis limits on measurement sensitivity. A a weak force acting system is determination classical parameter appearing in master equation that governs evolution system; limitations accuracy arise because it not possible distinguish perfectly among different values this parameter. Tools developed study and computation can be exploited improve precision physics experiments; examples include superdense coding, fast database...

We show that optimal protocols for noisy channel coding of public or private information over either classical quantum channels can be directly constructed from two more primitive information-theoretic tools: privacy amplification and reconciliation, also known as data compression with side information. do this in the one-shot scenario structureless resources, formulate our results terms smooth min- max-entropy. In context theory, shows essentially all two-terminal reduced to these...

Thermodynamics has recently been extended to small scales with resource theories that model heat exchanges. Real physical systems exchange diverse quantities: heat, particles, angular momentum, etc. We generalize thermodynamic exchanges of observables other than baths baths, and free energies the Helmholtz energy. These generalizations are illustrated "grand-potential" movements particles. Free operations include unitaries conserve energy particle number. From this conservation law from...

Abstract The quantum capacity of a memoryless channel determines the maximal rate at which we can communicate reliably over asymptotically many uses channel. Here illustrate that this asymptotic characterization is insufficient in practical scenarios where decoherence severely limits our ability to manipulate large systems encoder and decoder. In settings, should instead focus on optimal trade-off between three parameters: code, size devices decoder, fidelity transmission. We find...

Polar coding, introduced 2008 by Arikan, is the first (very) efficiently encodable and decodable coding scheme whose information transmission rate provably achieves Shannon bound for classical discrete memoryless channels in asymptotic limit of large block sizes. Here we study use polar codes quantum information. Focusing on case qubit Pauli erasure channels, to construct a which, using some pre-shared entanglement, asymptotically net equal coherent efficient encoding decoding operations...

The task of compressing classical information in the one-shot scenario is studied setting where decompressor additionally has access to some given quantum side information. In this hybrid classical-quantum version famous Slepian-Wolf problem, smooth max-entropy found govern number bits into which can be compressed so that it reliably recovered from and Combining result with known results on privacy amplification then yields bounds amount common randomness secret key systems using one-way...

We show that quantum-to-classical channels, i.e., quantum measurements, can be asymptotically simulated by an amount of classical communication equal to the mutual information measurement, if sufficient shared randomness is available. This result generalizes Winter's measurement compression theorem for fixed independent and identically distributed inputs arbitrary inputs, more importantly, it identifies a as gained performing it, input state on which performed. Our generalization reverse...

We construct new polar coding schemes for the transmission of quantum or private classical information over arbitrary channels. In former case, our scheme achieves symmetric coherent information, and in latter, information. Both are built from a construction capable transmitting channel. Appropriately merging two such classical-quantum schemes, one amplitude other phase, leads to similar Pauli erasure channels Renes et al. The encoding is entirely thus efficient. decoding can also be...

Quantum key distribution (QKD) protocols are cryptographic techniques with security based only on the laws of quantum mechanics. Two prominent QKD schemes BB84 and B92 that use four two states, respectively. In 2000, Phoenix et al. proposed a new family three state offers advantages over previous schemes. Until now, an error rate threshold for symmetric trine spherical code protocol has been shown trivial intercept/resend eavesdropping strategy. this paper, we prove unconditional protocol,...

A central goal in information theory and cryptography is finding simple characterizations of optimal communication rates under various restrictions security requirements. Ideally, the key rate for a quantum distribution (QKD) protocol would be given by single-letter formula involving optimization over single use an effective channel. We explore possibility such simplest most widely used QKD protocol, Bennnett-Brassard-84 with one-way classical postprocessing. show that conjectured false,...

Single-spin measurements on the ground state of an interacting spin lattice can be used to perform a quantum computation. We show how such mimic renormalization group transformations and remove short-ranged variations that reduce fidelity This suggests computational ability could robust property phase. illustrate our idea with rotationally invariant spin-1 chain, which serve as wire not only at Affleck-Kennedy-Lieb-Tasaki point, but within Haldane

Error correcting codes with a universal set of transversal gates are desideratum for quantum computing. Such codes, however, ruled out by the Eastin-Knill theorem. Moreover, theorem also rules which covariant respect to action unitary operations forming continuous symmetries. In this work, starting from an arbitrary code, we construct approximate entire group local in dimension $d\phantom{\rule{4pt}{0ex}}(<\ensuremath{\infty})$, using reference frames. We show that our capable efficiently...

We show that three principle means of treating privacy amplification in quantum key distribution, private state distillation, classical amplification, and via the uncertainty principle, are equivalent interchangeable. By adapting security proof based on we construct a new protocol for distillation which prove is identical to standard amplification. Underlying this approach characterization states, related their formulation by gives more physical understanding distribution.

We construct a channel coding scheme to achieve the capacity of any discrete memoryless based solely on techniques polar coding. In particular, we show how source polarization and randomness extraction via can be employed "shape" uniformly-distributed i.i.d. random variables into approximate distributed according capacity-achieving distribution. then combine this shaper with variant coding, constructed by duality capacity. Our inherits low complexity encoder decoder It differs conceptually...

Recently spherical codes were introduced as potentially more capable ensembles for quantum key distribution. Here we develop specific creation protocols the two qubit-based codes, trine and tetrahedron, analyze them in context of a suitably-tailored intercept/resend attack, both standard form, ``gentler'' version whose back-action on state is weaker. When compared to unbiased basis protocols, BB84 six-state, distinct advantages are found. First, they offer improved tolerance eavesdropping,...

We show that the tasks of privacy amplification against quantum adversaries and data compression with side information are dual in sense ability to perform one implies other. These two most important primitives classical theory, shown be connected by complementarity uncertainty principle setting. Applications include a new formulated terms smooth min- max-entropies, as well conditions for approximate error correction.

We construct a new entanglement-assisted quantum polar coding scheme which achieves the symmetric coherent information rate by synthesizing "amplitude" and "phase" channels from given, arbitrary channel. first demonstrate for with qubit inputs, we show that data can be reliably decoded O(N) rounds of successive cancellation, followed N controlled-NOT gates (where is number channel uses). also find entanglement consumption code vanishes degradable channels. Finally, extend to multiple inputs....